Adaptive controller having optimal filtering

ABSTRACT

A self-adaptive controller for use in a control process for providing ordered changes in a manipulated process variable in response to measured changes in a controlled process variable having means for using measured and predicted values of the controlled variable to obtain an estimated value of the controlled variable which estimated value is used via a selfadaptive controller to determine the change in manipulated variable. The controller is described with reference to a paper manufacturing process for controlling the basis weight and moisture content of a continuous web of paper.

IJnited States Patent [1 1 Chan et al.

[75] Inventors: Henry H. Chao; Michael G. Horner both of WisconsinRapids, Wis. Attorney-Lee Gary et [73] Assignee: Consolidated Papers,Inc., 57 ABSTRACT wlsconsm Rapids A self-adaptive controller for use ina control process [22] Filed: June 23, 1971 for providing orderedchanges in a manipulated process variable in response to measuredchanges in a [21] Appl' 155539 controlled process variable having meansfor using measured and predicted values of the controlled vari- [52]U.S. Cl ..235/151.1, 235/150.l, 162/253 able to Obtain an estimatedvalue of the controlled [51] Int. Cl. G05b 13/02 variable whichestimated value is used via a self- [58] Field of Search 235/150.1,151.1; adaptive controller to determine the change in manip:

162/252, 253 ulated variable. The controller is described with referenceto a paper manufacturing process for controlling [56] References Citedthe basis weight and moisture content of a continuous UNITED STATESPATENTS Web of p p 3,687,802 8/1972 Rummel et a1. 235/1513 X 28 Claims,Drawing Figures I i/GAIN CHANGE) I i K (Kit L PREDICTED M00 VALUE LOG/Cu M EL r0 ADAPT k1. Y HUK I) MODEL 40 L f (55 TPO/NT) D (PROCESS N(ERROR) "5 5?. mom I? s CONTROLLER PROCESS gfrl ngl.

C x I PL A N T I Z F s/ 1 P mmsunso VALUE) ADAPTIVE CONTROLLER HAVINGOPTIMAL FILTERING 3,619,360 11/1971 Persik, Jr. 235/l5l.1 X

Primary Examiner-Eugene G. Botz PAIENIEDOm23 mu 3.757.900

(INCREASE) (050175455) (N0 CHANGE) K(K+/)=K(/0f$ K(KH)=K(K)-$ MIG/k KmINVENTORS HENRY CHAO MICHAEL 6. HORNER PAIENIEuum 23 ms 3. 7 67 900 sum3 [3F 7 FIG. 4 W MEASUREMENT Z (Ir) 0 o o FRED/CANON YUM/w x k x BESTEsr/MArE Y/lr/lr} K TIME CONTROLLED VAR/ABLE Y E E F765 I i EIGAINCHANGE) I i x110: I [57E]? TED I,'.L.0-6IE"\ I L "if? 'r0 ADAPT M11 Irim/K MODEL 40 L (sE rpomr) D (PROCESS N (ERROR) I [I mom R CONTROLLERPR0cEss 33 gf g c x PLANT I 2 F s/ i P (MEASURED VALUE) (HES r EsTIMATE) Y! K /K) nv VENTORS HENRY CHAO ATTYS.

ADAPTIVE CONTROLLER HAVING OPTIMAL FILTERING BACKGROUND OF THEINVENTION 1. Field of the Invention This invention relates to processcontrol systems, and more particularly to a self-adaptive controller forsuch systems which provides analog or digital control signals to effecta desired response based upon a given process model.

2. Description of the Prior Art The availability of real time computersfor application in the process control field has made the implementationof sophisticated digital process controllers both possible andpractical. However, such process controllers have not been applied toprocess control on a large scale.

More specifically, as a result of the complex nature of many physicalprocesses, it is difficult to define relationships between variables ofthe process so as to permit control of the process operations to berelinquished to a digital computer. For purposes of analysis or controlof a process, theprocess dynamics must be inentified by identifiedmathematical model in the form of an equation or algorithm which definesa functional relationship between a controlled variable and a manipuvlated variable in the process control loop. The mathematical model mustaccount for variations such as changes in ambient conditions, changes inoperating conditions of apparatus, tolerances in materials used, etc.

In many processes, it is impractical to obtain a detailed model for eachcontrol loop because the processes cannot be adequately modeled usinganalytical methods. Therefore, in such cases, process identification isa necessary step in building an empirical mathematical model. The usualapproach for process identifcation can be a tedious procedure and,moreover, a significant upset has to be introduced intentionally intothe process. In addition, the mathematical model obtained throughprocess identification will be adequate at one particular operatingcondition, but when conditions change, the process may have to bere-identified or the performance of the control loop may becomeunsatisfactory.

In process control there are two major factors which contribute tounsatisfactory performance on the part of a control loop. One factor isnoise in measurement, and the other factor relates to changes inparameter values resulting from changes in operating conditions.

In any control loop, it is essential to have a measuring instrument tomonitor the controlled variable. Unfortunately, almost all measurementsare subject to error or noise because of inherent instrument noise,limited precision of the measuring equipment, the method of obtainingthe data, and/or process upsets that are too high in frequency to becorrected. If high noise levels are not accounted for in designing acontroller, disturbances will be introduced into the process due torandom movements of the manipulated variable caused by spurious noise.

conventionally, there are two approaches to take in compensating fornoisy signals. The first is to design the controller to be rathersluggish and the second is to use an external filter (analog ordigital). However, in both of these approaches, the effects of processdisturbances as well as noise are attenuated and compensation for realprocess upsets is delayed. For a system with a high noise-to-signalratio and fixed sampling frequency both approaches fail to provide asatisfactory solution. Ideally, a controller should respond fast to aprocess upset while ignoring noise. Such a controller can be obtainedwhen means are provided to distinguish between noise and true processupsets.

In addition to noisy measuring signals, most processes exhibitnon-linear operating characteristics caused, for example, by valvebacklash, long transportation delays, etc. Such factors account for thetypical non-linear characteristics of most processes, and ignoring themmay cause a control loop to become conditionally unstable.

One way to account for such factors is through the use of adaptivecontrol. Several adaptive control techniques have been developed inrecent years based on the use of statistical decision theory in controlsystems, including, for example,the parameter tracking method and thepattern recognition technique. Most of these approaches are generallyunsatisfactory, however, because they are too complex mathematically orare based upon assumptions (such as no signal noise, no sloppiness inactuators) that are unrealizable in a real process.

SUMMARY OF THE INVENTION The present invention provides a method andapparatus for an adaptive controller for use in a control process whicheffects ordered changes in a manipulated process variable in response tomeasured changes in controlled process variables.

In accordance with the adaptive feature of the controller, processidentification is not necessary to permit a process model to beobtained. The design of the controller is thus simplified because arough first estimate of a process model can be used, and throughsubsequent monitoring of the controller operation, the accuracy of theinitial estimate can be determined and new process parameters can beestablished if necessary. Therefore, it is not necessary to know thephysical relationships between all of the process variables.

The adaptive controller of the present invention utilizes a noveloptimal filtering technique which permits discrimination betweenmeasuring noise and true process upset such that the controller willrespond quickly to a process upset but will ignore measuring noiseinherent in most measuring arrangements.

To this end, a predicted value for the true state of the controlledvariable is obtained using the process model, and this predicted valueis used together with the actual measured value of the controlledprocess variable to obtain an estimated value of the true state of thecontrolled variable.

The estimated value obtained is used as the input to the controllerrather than the measured value to minimize the the effects ofmeasurement noise. Thus, the controller is enabled to respond to changescaused by true process upsets and to be substantially insensitive tomeasurement noise without introducing undue delay in recognizing processupset.

The controller is adapted to compensate for changes in parameters of theprocess by adjusting the process model. The model is tuned slowly inincrements within predetermined limits and only if there is asignificant difference between the predicted value and the past bestestimate of the controlled variable. Thus, it is not necessary tore-identify the process to retune the controller since controllerresponse is based upon the process model used.

One embodiment of the invention uses a digital computer and associatedcontrol programs to implement the adaptive controller. The programsdirect the digital computer to read the current value of the controlledprocess variable and to compute an estimated value for said controlledvariable.

The estimated value thus computed is used in the computation of anadjusted value for the manipulated process variable. In addition theestimated value (of the controlled variable) and the adjusted value (ofthe manipulated variable) are used in making adjustments to the modelwhen needed to provide a better predicted value for the controlledvariable used in the computation of subsequent estimated values of thecontrolled variable.

Under program control, the computer adjusts the gain of the processmodel and thus the process controller through a logic routine whichcompares predicted and estimated values of the controlled variable andadjusts the gain within high and low limits in accordance with the valueof the predicted value relative to the estimated value. The gain isincreased or decreased depending on whether the estimated value is lessthan or greater than the value of the predicted value.

In one embodiment, the method and apparatus of the adaptive controllerare described specifically with reference to an application in a papermanufacturing process to control basis weight and moisture.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of afeedback control loop for an ideal controlled process;

FIG. 2 is a block diagram of a feedback control loop for a physicalprocess characterized by process upset and measuring noise;

FIG. 3 is a flow chart for the logic of gain adaption for an adaptiveprocess controller provided by the present invention;

FIG. 4 is a graph showing the relationship between measured values of acontrolled process variable and predicted and estimated values of thecontrolled variable;

FIG. 5 is a block diagram of a process control system including anadaptive controller and optimal filtering provided by the presentinvention;

FIG. 6 is a flow chart for a computer program embodying the adaptivecontroller of the present invention;

FIG. 7 is a schematic diagram of papermaking apparatus controlled by theadaptive controller provided by the present invention;

FIG. 8 is a block diagram of a feedback control loop for a basis weightcontroller provided by the present invention;

FIG. 9 is a flow chart for a computer program for controlling basisweight and moisture content of paper in a paper manufacturing process;and

FIG. 10 is a block diagram ofa feedback control loop for a moisturecontent controller provided by the present invention.

GENERAL DESCRIPTION Introduction In the feedback control loop shown inFIG. 1, a controlled process variable Y of a process P varies inaccordance with changes in a manipulated variable X which are introducedinto the process by a process controller C. The error E is thedifference between the value of a setpoint R and the true value of thecontrolled variable Y. The adjustment made on the manipulated variable Xis related to the error E by a functional relationship specified in thecontroller. If the controller is properly designed, the adjustment willmove the controlled variable to the setpoint, and the value of thecontrolled variable Y will remain equal to the value of the setpoint R.

The input E to the controller C is the difference between the value ofthe setpoint R and the value of the controlled variable Y. When thisdifference is zero, the error E is zero, and thus the input to thecontroller is also zero. On the other hand, any positive or negativedifference between the setpoint R and the controlled variable Y willprovide an input of corresponding sign to the controller, causing thecontroller to adjust the value of the manipulated variable X tocompensate for said difference.

From the block diagram shown in FIG. 1, we can derive the overalltransfer function:

)/l C( where C(s) is the controller transfer function and P(s) is theprocess transfer function which is obtained by identification.Therefore, if the left side of equation (1 the ratio of the controlledvariable to the setpoint, is specified, the equation can be solved forC(s).

The identification of the process transfer function P(s) can beaccomplished by making a substantial step or pulse change in themanipulated variable X, and then recording both the manipulated and thecontrolled variables. Next, by assuming a form for the transfer functionand using linear or non-linear regression techniques, parameter valuescan be found which will minimize the sum of the square of the errorbetween the experimental response and the model response.

A simple and practical form of transfer function, which is often used inthe process industry, is the first order lag with dead time. Thetransfer function of such a model in Laplace transform notation is:

(2) Y(s)/X(s) P(s) (K/1's l) e where K is the gain, and land D are thetime constants and the dead time, respectively.

Since digital control is discrete by nature, the Z transformation with azero order hold is used instead of the Laplace transformation. Theequivalent expression in this case is:

(Z)/ (Z) (Z) 7) fl where 1; exp (-T/r), I= D/T, and T is the samplingperiod.

alte nateform of Equation (3) is: I

)-n (z) K(1 1;)Z- X(z) By definition, the Z operator, Z Y(z) stand forthe value of Y one sampling period ago, Z Y(z) stands for the value of Ytwo sampling periods ago, etc. The equivalent recursion formula forequation (4) is:

It should be pointed out that equations (2-5) are equivalent expressionsin different notation. In equations 2-5, three parameters namely, thetime constant *r, the dead time D, and the gain K define the functionalrelationship between the manipulated variable X and the controlledvariable Y. These parameter values are obtained through identificationof the process.

A simple and reliable form for the closed loop transfer function inLaplace transform notation is:

(6) Y(s)/R(s) (Ae /s s A) where D is the process dead time and is thereciprocal of the desired closed loop time constant. In Z transformnotation (with zero order hold) the above expression becomes:

Using the block diagram shown in FIG. 1, the overall transfer functioncan be related to the process P(z) and controller transfer functionsC(z) by the following expression:

By combining equations 3, 7, and 9 and solving for C(z), the controllertransfer function, the following expression is obtained:

But C(z) defines the transfer function between X(z) and 5(2),

Hence by combining equations 10 and 11, it can be shown that:

Where X(k) the manipulated variable X,

E(k) The difference between setpoint R and measured value or controlledvariable Y X(k-l) the past value of X(k) E(kl) the past value of E(k)X(k-F-l the value of X(k) at (l"+l sampling intervals ago K process gainF the equivalent number of sampling intervals for dead time 17exponential function of open loop time constant 0 an exponentialfunction of A as given in equation (8) Equation (13) is the recursiveformula for a digital controller C(s) and defines the desiredrelationship between the manipulated variable X and the controlledvariable Y.

The Noise Problem and the Optimal Filter Most control applications inthe process industry are characterized by two major difficulties. Onedifficulaty is measurement noise, and the other is changes in parametervalues due to changes in process operating conditions.

As shown in the process control loop of FIG. 2, the input E to thecontroller C from summing point 5, is determined by the differencebetween the value of the setpoint R and the value of a best estimate ofthe true state of the controlled variable Y. As will be shown, the bestestimate of the controlled variable Y is obtained through the use of anoptimal filter F which supresses the level of noise without losingsignal fidelity. That is, the best estimate of the controlled variable Yreflects true process upsets D while minimizing the effects of measuringnoise N.

As can be seen in the block diagram of FIG. 2, the process upset D isintroduced at the summing point S and for purposes of analysis is addedto the value of the manipulated variable X to form a total change U.

The measuring noise N is indicated as being introduced at summing point8, at the output of the process P and at the point at which measurementof the controlled variable Y is made, providing measured value Z for theprocess variable Y.

Without the use of the optimal filter F which has been provided by thepresent invention, the measured variable Z which is used to determinethe input to the process controller C would reflect not only trueprocess upsets D but also measuring noise N which is introduced into thesystem due to the inefficiencies of the measuring instruments, etc.

In any control loop, it is essential to have a measuring instrument tomonitor the controlled variable Y.-Unfortunately, most measurements aresubject to error or noise caused, for example, by inherent instrumentnoise, limited precision and reproducibility, the method of obtainingthe data, and signal fluctuations which are at too high a frequency tobe corrected.

It is desired that the controller C respond quickly to a setpoint range,and reasonably fast to a process upset, while ignoring high frequencynoise. Accordingly, the optimal filter F is introduced into the controlloop between the process output and the input to the process controllerC to provide a signal input to the control which reflects true processupsets D while minimizing measuring noise N.

In the system represented by the block diagram of FIG. 2, the processupset D is a random walk type of disturbance (i.e., the integration of awhite noise), and the measuring noise N is white noise. The transferfunction of the process P is given by equations (2) and (3) and theequation for the controller is (13).

The following relationship can be derived from the block diagram of FIG.2 and equation (3):

(Z)/ (Z) (Z) /1 r) which can be rewritten in the recursive form as:

Substituting the index K-l for the index K in equation (15) gives:

(16) Y(k-l) K( ln)U(kl'-2) 'nY(k2) which if subtracted from (15) gives:

(17) AY(k) K( l1;)AU(kl"-l) nAY(k-l) where the notation A stands for thedifference between two consecutive values. Hence, if we know AU(kl" l)and AY(kl then from equation (17) we can predict AY(k).

From FIG. 2 it is apparent that the value for the process controlvariable U is the sum of the manipulated variable X and the processupset D or;

Since the process upset D is a random walk type of disturbance, AD iswhite noise and the best estimates of the difference between successivemeasurements is zero. Therefore,

(19) AU(kI-l/kl"l) AX(k-l"l) where the notation at the left means theestimate of AU at (k- F-l )th period, with all information available upto (k-F-l )th period. In general, Y(i/i-j) means the estimate of thevariable Y at i, with information available up to i-j period, e.g.,Y(i/i-l) indicates the predicted value of Y(i) without the presentmeasurement, and

Y(i/i) is the best estimate of Y(i) with the present measurement alongwith all the previous information.

Using the estimate for the true state of the controlled variable Y, andtaking advantage of the relationship expressed in equation 19), it canbe shown that equation (17) becomes:

(20) AY(k/kl) K(l-'n)AX(kl"l) nAY(- k-l/k-l) where Y(k/k-l) is apredicted value for Y(k), and AY(kl/kl) is the difference betweensuccessive best estimates of the true state Y(k). By definition:

AY(kl/k-l) Y(k-l/k-l) Y(k-2/k-2) from equations (20) and (21 thefollowing is obtained:

There are two values with which to work in getting a best estimate ofY(k/k); one is the predicted value Y(k/kl) and the other is themeasurement Z(k). The predicted value Y(k/k-l) does not reflect thecurrent process disturbance D (FIG. 2) or the measurement noise N. Onthe other hand, the measured value Z(k) is affected by both parameters.

A way to infer the best estimate Y(k/k) from the predicted valueY(k/k-l) and the measured value Z(k) is theorized as follows: If thereis no disturbance and no measurement noise, then the predicted valueY(k/k-l) should agree with the measurement Z(k). Because of processupset D and measurement noise N, however, the measurement Z(k) deviatesfrom the predicted value Y(k/k-l This variance may be broken into twoparts representing a process upset factor 0 which results from thedisturbance and the measurement noise factor 0 which results frommeasurement noise, 1.e.,

The measurement noise factor 0 is the variance evaluated from a sequenceof measurements while the process is running its steady state condition.The process upset factor 0 is the squared deviation of the measurementfrom the setpoint minus the measurement noise factor 0 By definition thevariance of the difference between the true state Y(k) and theprediction Y(k/k-l) is:

0 where e is a statistical expression for the expected value.

Also by definition, the difference between the true state Y(k) and themeasurement Z(k) is:

Since the value of Y(k) is not known accurately, there is no way toevaluate either the process upset factor 0- or the measurement noisefactor of directly. If the measurement noise factor U is much largerthan the process upset factor 0' however, the best estimate Y(k/k)should be very close to the prediction Y(k- /kl). On the other hand, ifthe measurement noise factor of is much smaller than the process upsetfactor 0' then the best estimate Y(k/k) should be very close to themeasurement Z(k). In general, the best estimate Y(k/k) should liebetween the measurement Z(k) and the prediction Y(k/k-l A preciseformula which satisfies the above description is as follows:

/k) Y( W where W is a noise weighting factor defined as:

(27) W (7 ((1,, of) and where the value Y(k/k) represents the bestestimate of the true state Y(k) with all the information available up tothe kth sample.

The value of the noise weighting factor W can be obtained by collectinga sequence of measured values and using equations (22) and (26) toobtain an average value for the noise weighting factor W. A typicalvalue for the noise weighting factor W is 0.3.

Adaptive Controller The process controller C (FIG. 2) is designed togive a desirable overall response based upon a given process model. If,however, the process behavior changes, the actual overall response willdeviate somewhat from the expected response. When the difference betweentrue process behavior and the process behavior predicted by the modelbecomes great enough, the control loop may become unstable. Accordingly,it is desirable that the controller C be adaptive to changes in theprocess. One way to retune the process controller is to reidentify theprocess. However, the identification procedure is quite time-consumingand a substantial process upset has to be intentionally introduced intothe system. An ideal way is to identify the process while the process isunder closed loop control.

This approach is obtained in accordance with the adaptive controller ofthe present invention in which a technique is proved for adapting theprocess model to changes in the process behavior.

The equation for the digital controller C was given by equation (13)which is repeated below:

Equation l 3) relates the values for the present error E(k), previouserror E(k-l) and previous manipulated variable settings X(k1 and X(kIl)to the present value required of the manipulated variable X.

Since previous values of the manipulated variable X and the controlledvariable Y are known, a predicted value Y(k/kl) can be obtained fromequations (22) and (5) and is given by the following equation:

(29) Y(k/k-l) [((k-l )(1-17) X(kl"l) 17Y(- k-l) where K(kl is the gainestimated at the previous time. When there is no disturbance ormeasuring noise, the measurement will be the true state Y(k) which canbe evaluated by the following equation:

The value of the true state Y(k) should agree with the value for thepredicted value of the true state Y(k/k-l provided that the process gainK does not change. lf the value of the true state does not agree withthe predicted value for the true state Y(k/kl then the gain of thesystem can be adjusted accordingly using the following relationship:

A real process is different from an idealized system in that in a realprocess there are always disturbances and measuring noise which willcause the measurement to deviate from the predicted value Y(k/k-l Inaddition, not only the gain but also the time constant of the controlloop will vary. Furthermore, the process dynamics may not exactly fitthe model which has been assumed for the process.

To compensate somewhat for these limitations introduced by disturbanceand noise, the value for the best estimate Y(k/k) is used rather thanthe value of the direct measurement Z(k). In addition, the model isretuned only if there is a significant difference between the predictedvalue Y(k/k-l) and the past best estimate Y(kl/kl Furthermore, the gainof the model is adjusted slowly and gradually using incremental changesuntil the desired gain is obtained, and an upper and lower limit is setfor the gain adjustment.

Digressing for a moment, consider the variation in the time constant ofthe process model. It is not necessary that the model describe thedesired process exactly due to the adaptive feature of the controllerwhich is afforded by making the model tunable. If the gain isoverestimated, the response will be more sluggish than expected, and ifthe gain is underestimated, the response will be overactive. Simulationstudies show that for controller design purposes, a change in timeconstant may be approximated by a change in gain. Accordingly,compensation for gain changes will automatically compensate fordeviations in time constant.

Consequently, it is only necessary to tune the gain to make thecontroller adaptive. The logic for adaptive tuning is shown in FIG. 3.

Referring to the flow chart of logic gain adaptation given in FlG. 3,first the difference between the predicted value Y(k/k-l and the pastbest estimate of Y(- kl/k-l of the true state Y(k) is compared to avariation standard VAR. If the difference between the predicted valueand the past best estimate is less than VAR, no change will be made inthe gain. The variation standard VAR should be approximately twostandard deviations of the measuring noise.

if, on the other hand, the difference between the predicted valueY(k/k-l) and the past best estimate is greater than VAR, the predictedvalue will be compared to the best estimate to determine if the gainshould be increased or decreased.

To avoid introducing a sudden substantial change in the loop gain, thegain is increased in 2 percent increments of the gain factor (G). Inaddition, limits ranging from 20 to 50 per cent are set on the amount ofchange allowed to the gain.

Our digital controller is defined by equation (13) from which it can beseen that the manipulated variable X is related to the error E by thereciprocal of the process gain K. Therefore, the controller is adaptedto an operating condition change, when the process model is adjusted viaits gain to reflect said change.

in FIG. 4, there are shown three sets of points representing measuredvalues Z(k), predicted values Y(k- /kl and best estimates Y(k/k), theweighted average of the measured value and the predicted value.

Whenever the predicted value is greater than the best estimate and thereis a significant difference between the latest prediction and the lastbest estimate, such as at point I, the gain will be decreased such thatthe predicted value will approach the estimated value.

At point I], where the predicted value is less than the best estimateand there is a significant difference between Y(k/kl) and Y(k-l/kl) thegain will be increased. At point Ill, where the predicted value is lessthan the best estimate, but there is not a significant differencebetween the prediction, Y(k/k-l and the past best estimate Y(kl/kl thegain will not be changed, because said difference is not due to modelerror but caused by a process upset or measurement noise.

In summary, the logic of gain adaptation operates as follows: First, thepredicted value is compared to the past best estimate, to see if asignificant difference exists between them. If there is, the predictedvalue is then compared to the best estimate to determine whether theestimate lies above or below the predicted (model) response. The modelgain is then incremented accordingly.

in the illustrated embodiment, the gain is increased or decreased inincrements of 2 percent within specified limits. Thus, the differencebetween the prediction and the best estimate determines the direction ofthe 2 percent gain change provided that the predicted value Y(k/k-l)differs sufficiently from the past best estimate Y(kl/kl Whenever thepredicted value Y(k/k-l) shows less change than the best estimate theprocess gain is increased and if the best estimate shows less changethan the predicted value the process gain will be decreased.

DESCRIPTION OF A CONTROL PROCESS USING ,THE ADAPTIVE CONTROLLER ANDOPTIMAL FILTER Referring to FIG. 5, there is shown a block diagram of asystem control loop including adaptive tuning of the model and optimalfiltering. in the block diagram of FIG. 5, the bold line indicates thebasic feedback loop including the controller C and the physical processP or plant which is controlled by the process controller. The controlleris defined by equation (13) which is repeated here:

0/K(l'n)][ 7 6X(kl) (l-6)X(k-Il) where K, n, and F are parametersdeveloped from the model and 0 is an exponential function of the desiredclosed loop time constant.

As is the case in the block diagram of FIG. 2, the error input E to thecontroller is the difference between the setpoint R and the bestestimate of the controlled variable Y(k/k) which is obtained through theuse of the optimal filter F which operates to distinguish between trueprocess upsets D and process measuring noise N.

The light lines implement the optimal filter F wherein the predictedvalue Y(k/k-l) depends upon the previous best estimate Y(k-l/kl) and theoutput X(k) from the control algorithm in accordance with therelationship given by equation (22), which comprises the process modelM.

The inputs to the optimal filter F are the measured value Z(k) and thepredicted value Y(k/k-l) which is determined from the model.

The best estimate is the weighted average of the predicted valueY(k/k-l) and the measurement Z(k) as given in equation- ('26):

' (26) Y(k/k) Y(k/k-l) W [Z(k) Y(k/k-l) where W is a weighting factor.

The dashed lines in the block diagram of FIG. 5 show the adaptive tuningfeature implemented by the adaptive gain control logic (FIG. 3) whichtunes the model M.

Since our controller ('see equation (13)) contains the model gain K asan integral part of its structure, controller tuning is automatic whenmodel gain is adjusted adaptively.

The adaptive controller comprising the controller C, the optimal filterF, the mathematical model M and the model gain adaption logic L providedby the present invention can be implemented either by a digital computerand associated software (represented by the block 40 in FIG. 7) or byhard wired logic employing BRIEF DESCRIPTION OF THE CONTROL SUB-ROUTINEThe statements which comprise the OPCON control subroutine are given inTable I. It is seen that the proappropriate logic circuitry. In thepreferred embodi- 5 gram proceeds with comment statements each led by "1using acomrol subroutine k as h OPCON the letter C, which gives thepurpose, usage, and dedigital controller. The program is WIIttIeI'IIHFortran scription of the parameters of the program, followed by languageand a subroutme for a mamhne process functional statements whichindicate the operations to control program. The OPCON program can bestored be performed A as part of a general purpose control library andcan be 10 Briefly referring to the program flow chart given in used invarious controlled processes via changes in the Fla 6, the subroutineuses equation (26) to compute arguments 9 the Fortran can from themainline a value for the best estimate Y(k/k) of the true state of gram.That Ts, the arguments of the Fortran sub-routine the controlledvariable Y from a weighted average of contain all the information neededto define the prothe predicted value Y(k/k 1) and the measured valuecess to be controlled, therefore, this sub-routine is 15 Z0) using thefollowing relationship: completely generalized and can be used by anynumber 7 of mainline control programs just be redefining the ar- (26)YBEST YPRD W(YMESU YPRD) guments of the CALL. A program flow chart forthe OPCON control sub-routine is given in FIG. 6 which As has beenmentioned above the best estimate flow chart contains all the essentialequations and logic 20 YBEST is used to represent the controlledvariable f the Optimal filt the adaptive tuning and the com rather thanthe actual measured value YMESU in order UOTTCL to minimize the effectsof measurement noise.

TKEITE T WW V W OPCON SUB-ROUT INE k c suHRLTuTTNE OPCUN c c PURPHSE (3IN SF-LF AaAPTTvE coNTHTTLLER FOR ME TN A ccv Tl l 7 lf l .Cl-$$ Eji cTwnvmwc CHANGtS IN A MANIPULATED vAE T AHLF. X1 TN RESPLTNSE c TU MEASUtU CHANGES TN A ELTNTHLTLLED VARIAQLF .Y.HAvTNc NEANs c FllR TTsTNcMEASUREMENTS AND PREDICT IONS TTE THE (.fNTROLLE-D 0 VA? AHL E TULTETTATN THE BEST ESTIMATE OT- THE CONl'PULLEL) vAHT- c ABLE, HHTcH ISUSED To Ul: TERM TNE THE LHANGE TN MANIPULATE!) c VARIABLE c c USAGE ccALL OPCONI YNEsu, YSP ,YPRTT, YBEST ERR x, x1 T UT ,TALTTT. TAuT; sEsT. c GTUNF ,GHI ,(BLO, 005, HT c c OESCR l PT T 0N llF PARAMETERS cTNT-5U MEASURED vALuE TTE THE cnN TRTTLL LD V l A5L E c vsr sE T PUINTOF THE CUNTROLLED VARI ATTLE T, YPDI) DRFUIC TED VALUE OF THEcnNTHTTLLT-n VANTAHLE 0 Eu: ERROR BETNEEN THE W T PUINI ANTT THE TEsT E5T MA T F TE c THl: LUNTRLTLLED VARIABLE c x THE Dt sTRATTLE sETTTNT; OFTAN I PULATFD vAHTALTLE c Xl AN ARFJAY LTT- PREvmTTs Sl-Tl TNT,s IlF NANT DULATEI) VAT c ABLE NT TH A DI 'lFNS TLTN .JF lDT+l T c TNT DEAD TTNEFACTUR DEAD T T NE S/WPL I No PER I'JI) c TAuu FUNCTIUN TTE CPFN LllLlPTT NL CONSTANT c Ex -SA=4PLING PERIOD OPEN Loo TTNE c TNsTANT T c TAUCFUNCTION Ofcms ED LOOP TTNE coNsTANT T c EXP l -SAMPL [NG PERIOD CLOSEDLOOP T WE cTTNsTANTT c GFST TN TT TAL EsT T NATE llf- STEADV sTA TE GAlN TTE [WI-EN THF c NANTPuLATEo VARIABLE ANT) THE CllNTROLLtD vAHTAHLE ic cTuNE TUNING PARAMETER c GHI UPPER LIMIT OF TUNE f c GLO LUWER LIMIT0F GTUNF 0 cm oEAo TSAND FUR TUNING c N .TE mH I NC FAC IUK c c REHATTKc NHEN ON "IANUAL sET c YPRD YSP c YBEST vsP C EQQ 0 c (JUNE 1 o c XIPRESENT SETTING E THE MAN IPULATED VAR l AHLE Table l Continued C y iTH; FI'JLLDW ING PARAMEThRS SHOULD 0F; s/IvF I IN MEMORY C YP D YQESIERF XI DTUNF C I, SUBPHUTINES- ANu FUNCTION SUBIZUUTlNtS FIIIJI IEII cAHS c C .I' 'Il0......I.... t: II!.IQ..DO...QIQI'FICOII.UOIIIII I c 0001SUHRUUTINE 0PCIJI\HYMESU,Y$P1YPRU, YdESTqERlhX Xl ,IIJrJ/IumTAumGEsrI 1cnmemm .0L0,00B.III 0002 DIMENSION x1 I ll c HISTUR ICAL SHlFT c 0003BEST2=YBEST 000 ERRZ =EPR c 0 TH& HtST ESTIMATE IS. A WEIGHTING AVERAGE0F MEASUREMFNT c AND PREDICT mm C 0005 YHEST=YPQD +w =I YMtSU- YPRuI c0000 ERP=YSP YIJEST 0001 0AIN=0Fsw0 uME 0008 x=I 1.41100 I /,Il.TAU0l/GA[N*( ERRTAUU*ERR2)+TAUC*XI I II 1 H I .-TAUC)*XI I IUTH) 0009YPRDO=GAIN H l.-TAUC)*( Xl I IDTI-XI I 1on1 I I +TAUD*(VBESl-BEST? I+YBFST c 0 THE CONTROLLER wlLL BE ADAPTED IF A SIGNIF [CANT CHANGE HASI: 00000 ED 0 0010 IF I us I YPRD -'IEsr2 I- 00m 100. 10,10 0011 IF IYPRD-BESTZI I 100 I 0012 15 IF I YBEST-YPRD) 22, 11. 17 0013 17 GTUNEGTUNE-O 02 0014 lFlGTUNE-GLO) 1a 100, 100 0015 18 GTUNE 01.0 0010 00 I0100 0017 20 IF I YPIEST YPR III 17, 22. 22 0010 22 GTUNE (JUNE +0.020019 IF I GTUNE GHl I 100 I 100, 23 0020 23 GTUNE GHI c c HISTUQ. ICALSH [H c 0021 I00 YPRD YPRDU 0022 l=lIJT 0023 101 x I I 1+1 I=xI I I I0024 I= l-l 0025 IFI I I 102. 102 I 101 0020 102 x I I 1 I =X 0027RETURN 002a END The value of the error ERR between the setpoint R andthe best estimate Y(k/k) is determined using the following relationship:

The error which is the difference between the setpoint and the bestestimate is the input to the controller C and is one of the variables ofequation l 3) which defines the controller. For an initial value, theerror is set equal to zero.

Process gain GAIN is obtained by multiplying the initial gain estimateGEST by a gain tuning parameter GTUNE which is obtained through thelogic of gain adaptation. The initial value for the gain tuning factorGTUNE is one.

Then the error and gain obtained are used to com- T pute the value ofthe manipulated variable X using equation (l3): (13) X portion of theprogram computes a value for the gain tuning factor GTUNE.

The statements which comprise the Fortran language sub-routine arelisted in Table I. The Fortran program is made up of a series ofstatements, each of which is either in order to carry out some operationor a source of information regarding the program. The statements provideinformation about the program, particularly definition of variables andits usage. The instructions which relate to a specific application ofthe adaptive control sub-routine to the paper manufacturing process willbe described hereinafter.

APPLICATION OF THE CONTROLLER PROGRAM TO A PHYSICAL PROCESS The OPCONadaptive controller sub-routine is part of a main control program usedfor control by a digital computer such as an IBM Model 1800 processcontrol computer. Through its use a system of control algorithm in thecomputer is adapted in such a way that it is responsive to changes inthe parameters characteristic of the controlled process variables whichare measured by appropriate measuring apparatus, and the system ofalgorithms provide corresponding changes in the value of a manipulatedprocess variable X to compensate for deviations from a desired operatingcondition. 1

The constants and initial conditions required for the sub-routine OPCONare given in the mainline program via the arguments; the variable inputdata required to implement the scheme include the measured value YMESUand the setpoint YSP, both of which are obtained from outside sourcessuch as analog inputs and manual entry stations.

It is pointed out that the OPCON control sub-routine utilizes measuredvalues to compute desired changes in process variables. In addition,other sub-routines, which will be described hereinafter, are also usedwith the OPCON control program to affect adjustments of variables in thephysical process. 7

Specific Application of the Adaptive Controller t5 the Control of BasisWeight Equation (2) which de fines the control system trans ferfunctions, and equation (13), which defines the controller for thesystem, are applicable to any system in which the process dynamics arecharacterized by a first order lag with dead time, and thus the OPCONcontrol program is preferably used in systems so char acterized.However, it is pointed out that other higher order processes can beapproximated by a first order lag, and the adaptive feature of thecontrol system provided by the present invention will permit desirableclosed loop performance to be obtained in such system. By way ofillustration, the adaptive controller will be described in anapplication in a paper manufacturing operation to control the basisweight and moisture content of paper during the manufacturing process.

The schematic diagram given in FIG. 7 shows paper manufacturingapparatus 50 that is controlled by a digital controller using the OPCONcontrol sub-routine provided by the present invention. Briefly, in thepaper manufacturing process shown, the apparatus 50 forms a continuousweb or sheet of paper from a mixture of fibrous stock contained in aheadbox 21. The mixture is deposited in a continuous web onto aFourdrinier wire 22 as the wire passes about a breast roll 23.

Most of the water is drained through the wire into a white water silo 25as the paper web is conveyed on the wire 22 until the wire passes thecouch roll 26 at which point the paper leaves the wire and is fedbetween press rolls 27 and over dryers 28 for the removal of additionalmoisture. The finished paper web or sheet then passes onto the windupreel 29.

For purposes of control, this basis weight and moisture content of thepaper web are measured at a point between the dryers 28 and the takeupreel 29 through the use of a measuring apparatus including a beta gauge30 and an infrared sensor 31, to measure basis weight BW and moisturecontent MOI, respectively.

Basis weight is controlled by adjusting the consistency of the stocksuspension in the headbox 21. This fi spension consists of acontinuously flowing mixture of roughly 5,000 gallons per minute ofwhite water having a consistency of approximately 0.2 percent recycledvia a fan pump 32 from the white water silo 25,'

and roughly 500 gallons per minute of a thick stock having a consistencyof approximately 3 percent flowing through a stock flow valve 34 andinto said fan pump 32. When the setting X(k) of the stock flow valve(and thus the rate of flow of the thick stock into the headbox) ischanged, a corresponding change occurs in the total solids content ofthe mixture in the headbox. Such a change can be obtained withrelatively minute adjustments in the volume per minute flow of the thickstock. The setting X(k) of the stock flow valve 34 is the manipulatedvariable of the process control loop. Thus, the basis weight of thepaper being produced is controlled by adjusting the stock flow valve 34to allow less or more thick stock into the total flow line, thereby toadjust the consistency of the stock suspension in the headbox 21.

The basis weight is measured by a beta gauge 30 mounted on a scanningframe (not shown) located at the end of the dryer section 28 of theapparatus. A scanning frame and beta gauge for this purpose are wellknown in the paper manufacturing industry and such monitoring apparatusare shown, for example, in US. Pat. Nos. 2,750,986; 2,790,945; and2,829,268.

The beta gauge 30 carried on the scanning frame, is moved across thewidth of the paper web once every seconds and provides an output signal,ranging from 0-5 mv, which is proportional to the amount of betaparticles present in a beam after said beam has passed through themoving paper web 20 at the point of measurement and thus gives a goodapproximation of the mass of the paper web. The output signal providedby the beta gauge 30 is sampled every 2 seconds by a digital computer40, and the outputs provided by each 60 second scan are averagedproviding an average basis weight BW for each scan. The average basisweight is the controlled variable Y in the basis weight control loop,but its control is not achieved via the direct manipulation of the stockvalve. Instead, control is achieved via a cascaded control system with adry basis weight controller adjusting a dry stock flow (mass rate offlow of pulp to the machine 50) set point in the outside loop and a drystock controller adjusting the stock .flow valve in the inner loop isshown in FIG. 8. In this particular instance, both controllers areimplemented by digital algorithms in a process control computer with drybasis weight being defined as the basis weight BW measured minus the percent moisture content MOI measured and is given by the expression:

1'7 32 'DBW BW 100 MOI) 0.01

The process dynamics between the DSF controller and the basis weight andmoisture content measuring apparatus 30, 31 shown in the block diagramof FIG. 8, can be approximated by a first order lag plus dead time, andaccordingly, the setpoint X(k) of the DSF controller is given byequation (13:

7)] 7 X(kl) (1- 0)X(kI'1) where X(k-l X(k-2) are the two previoussettings of the DSF setpoint, E(k), E(kl) are the present and previousdry basis weight errors, that is, the difference between the dry basisweight setpoint DBWSP and the dry basis weight measured DBW, and K isthe process gain. Typical values for the process constants 0, 'r and Kobtained for one papermaking machine are as follows:

6 exp(-l"T) exp(60/100) Basis Weight Controller is" as 1555;;wightcofitiol'lr 'siiswazchaaiieaiiy in FIG. 8, the primary manipulatedvariable is the thick stock flow 49 supplied to the apparatus 50controlled by the basis weight controller 52 and dry stock flowcontroller 51 which together comprise the digital controller 40. Everyfour seconds, the consistency and flow rate of the thick stock aremonitored. The stock valve 34 is operated under computer control by anoutput of the dry stock flow controller 51 to give the desired dry stockflow (the product of consistency and flow rate). The target value orsetpoint R for dry stock is set by the basis weight controller 52 whichis comprised of the OPCON control program.

Thus, referring to FIG. 8, it is seen that a cascade control scheme isused in the control of basis weight, the basis weight being controlledby a first outer loop, and the dry stock flow being controlled by asecond inner loop.

by the address of the ECO used. Changes in valve position are calculatedvia the dry stock flow controller 51 using the dry stock flow setpointDSFSP as provided by the basis weight controller (OPCON program) and thedry stock flow DSF which is'obtained by multiplying the stock volumetricflow rate by stock consistency.

The dry stock flow setpoint is provided by the basis weight controller52. The input to the basis weight controller 52 is the differencebetween the basis weight setpoint BWSP and the basis weight measurementBW obtained through the use of the beta gauge 30 and infra red moisturesensor 31.

Summarily, the basis weight controller effectively comprises a cascadecontrol scheme. The first control loop (dry stock controller 51)controls actual valve movement as a function of dry stock flow change,and the second control loop, (the basis weight controller 52) controlsthe dry stock flow setpoint DSFSP as a function of drybasis weightchange.

The basis weight is proportional to the dry stock flow and inverselyproportional to the speed of the machine. Thus, the steady state gain Kof the basis weight and dry stock flow controller given in equation 13)can be e); pressed by the relationship:

(33) K [(constant) (stock consistency) (slope of valve curve)/(machinespeed) (machine width)] where the constant (a function of the paperprocessing machine) serves to convert fiber flow to basis weight so thatthe gain K can be expressed in units of pounds of basis weight pergallon per minute of thick stock flow change.

. In the basis weight controller (FIG. 8), the basis weight and moisturemeasurements provided by the beta gauge 30 and moisture gauge 31 (FIG.7) are used in equation (32) to obtain values of dry basis weight DBW,and the values obtained along with other required data, serve as inputsto the computer for the control sub-routine which will output thecurrent setting for RATIO defined by equation (37) to provide the drystock flow setpoint DSFSP for the dry stock flow controller 51 (FIG. 8).The dry stock flow setpoint DSF SP serves as an input to the dry stockflow controller 51 which together with the value of the dry stock flowwill affect the determination of a setting for the stock flow valve 34under the control of the dry stock flow controller 51.

The following description of a mainline computer program which is usedwith the OPCON control subroutine relates only to the basis weightcontroller 52 which outputs the dry stock flow setpoint DSFSP. A furtherprogram would be used to implement the dry stock flow controller 51which provides the output for effecting actual manipulation of the stockflow valve.

Equation (33) can be factored as follows:

(34) K K1- K2 (35) K1 dry stock flow/valve movement (consistency) (slopeof valve curve) where K1 is related to the process dynamics between thevalve controller 51 (FIG. 8) and the stock flow 49 (the operatingcharacteristic of the valve), and where (36) K2 dry basis weightchange/dry stock flow change (constant)/(machine speed) (machine width)is'felatedto the pmeess d nafiarc' 'sawanaernew 49 and basis weight (thedynamics of the papermaking machine). It is apparent that the product K1K2 represents the gain of the total process from the stock valvecontroller (51) to the basis weight. Furthermore, denoting the ratio(37) I RATIO change dry stock flow change/machine speed then fromequations (36) and (37):

(38) Dry basis weight change/RATIO change (constant)/machine width Theright hand side of equation (38) is constant for a given papermanufacturing machine with a typical value being 2,200.

V Mainline Program for Basis Weight Controller Xpr ogrn flow chart forthe basis weight controller is given in FIG. 9. Referring to FIG. 9, inthe basis weight controller operation, the basis weight measurement BW,basis weight setpoint BWSP, the moisture setpoint MOISP and themachinespeed are read.

Then a computer switch is tested to determine if the process is undermanual or computer control. When the switch is off the process is undermanual control and the basis weight program is bypassed. When the switchis on, the process is under computer control and a test is made todetermine whether or not this is the first pass. On the first pass theprogram branches to establish initial conditions to assure bumplesstransfer from manual control to computer control. The initial conditionsfor one example are given in the box 4 in the flow chart of FIG. 9 andone set of values for the constants is given in column B, Table 11.

After the first pass, when the initial conditions have been established,the program will read the measured values of basis weight BW and basisweight setpoint BWSP together with the measured values of moisture MOIand moisture setpoint MOISP to determine a dry basis weight DBW and adry basis weight setpoint DBWSP.

The dry basis weight and dry basis weight setpoint calculated are usedin the OPCON control sub-routine to provide the desired output settingRATIO.

This output setting RATIO will be used in the calculation of a dry stockflow setpoint DSFSP which will be used as an input for the dry stockflow controller 51.

. TAL LEJLW GLOSSARY OF TERMS A B C D E Basis Variable OPCON WeightMoisture used Argu- Control- Controlin the Remark ment ler ler textYMESU DBW MOI Z(k) Measurement YSP DBWSP MOISP R(k) Setpoint YPRD PBWPMOI Y(k/kl) Prediction YBEST BBW BMOl Y(k/k) Best estimate ERR EBW EMOIE(k) Error X RATIO STMSP X(k) Manipulated Variable -Xl RATl STMl X(kl)Previous values X(k2) of X lDT 1 1 F Dead time factor TAUO 0.301 0.606 1Function of open loop time constant TAUC 0.55 0.717 6 Function of closedloop time constant GEST 2220. GMOI Initial estimate of the gain GTUNE GBGM Tuning parameter for the gain Gl-ll 1.3 1.5 Upper limit for GTUNE GLO0.7 0.5 7 Lower limit for GTUNE GDB 0.25 0.05 VAR Dead band of tuner W0.3 0.3 W Weighting factor Moisture Controller After the basis weightcontrol loop operations have been completed, a similar sequence ofoperations will be performed for the moisture content controller 65shown in block form in the process control loop for moisture controlgiven in FIG. 10. The moisture controller 65 comprised of the OPCONcontrol subroutine which directs the digital computer 40 to execute adesired series of operations to read moisture measurements and calculatea setpoint for the analog steam pressure controller 69.

Referring first to FIG. 7, the moisture content of the paper web iscontrolled by adjusting the pressure of the steam in the dryer canswhich comprise the dryer 28. A change in the setting of the steampressure valve 60 to increase or decrease the steam pressure will causea change in the drying effect of the dryer 28 to remove correspondinglymore or less moisture from the paper web 20 as it passes through thedryer 28. The steam pressure valve setting is regulated directly by ananalog controller 69 of which the computer 40 has supervisory control.

The preferred moisture meter 31 for this application is an infraredreflectance meter type such as marketed by General Electric Companyunder the trademark Inframike II and is preferably mounted on a scanningframe together with a beta gauge such as the one mentioned above.

The infrared reflectance meter is moved across the width of the paperweb once every sixty seconds enabling it to provide a signal which, forexample, may range from approximately 10-50 ma, which signal isproportional to the per cent moisture in the paper. The moisture contentmay range, for example, from 0-12 percent.

To facilitate sampling, the current output of the infrared moisturemeter is converted (for example through the use of a ten ohm precisionresistor) into a voltage ranging, for example, from -500 MV. The

resulting voltage signal is sampled every two seconds, and the sampledoutputs provided for each sixty second scan are averaged, providing anaverage moisture content reading MOI for use by the supervisory digitalcontroller. The average moisture content reading M01 is the controlledvariable in the moisture content control loop.

Responsive to each moisture content reading provided, the digitalcomputer 40 determines the difference between the existing steampressure setpoint STMSP and the setpoint required to provide the desiredmoisture content for the paper web or sheet 20, and provides a pulsetrain, the number of pulses of which represent this difference. Thepulses are used to operate a stepping motor 61 which moves the setpointof the analog controller 69 controlling steam pressure in the dryercans. The steam valve 60 then is moved accordingly by the analogcontroller 69.

In moisture control, it is difficult to predict the gain K for acontroller since the process dynamics relating the steam pressure andthe moisture content cannot be determined analytically. However, inaccordance with the adaptive features of the controller program,provided by the present invention, the controller gain K can beestimated at a reasonable initial value and the moisture control loopcan be tuned under computer control using theOPCON control program.

Referring to FIG. 10, the input EMOI to the moisture congroller 65 isthe difference between the value of the moisture setpoint MOISP and thevalue of the moisture measurement MOI.

Responsive to the error input EMOI, the moisture controller 65 outputs asetting STMSP for the steam pressure will effect a corresponding changein the dryness of the paper coming from dryer 28 and thereby bring thevalue of the moisture measurement MOI into agreement with the setpointMOISP.

Assuming that the drying efficiency, defined as the additional moistureremoval per unit pressure increase, is inversely proportional to thepresent steam pressure, the following relationship can be obtained:

moisture change/pressure change (constant)/- steam pressure (psia) Forone paper manufacturing machine a typical value for the constant wasnine.

Moisture control is similar to the basis weight control described in theforegoing with reference to the flow chart given in FIG. 9, with theexception that different parameter values are used, therefore, thearguments of the FORTRAN sub-routine OPCON are different.

The values of the various constants for one example' 7 are given incolumn C of TABLE II, and the initial conditions are given in box 10 ofthe flow chart of FIG. 9.

Summary From the foregoing description, it is apparent that the presentinvention has provided a method and apparatus for an adaptive controllerfor use in a control process which effects ordered changes in amanipulated process variable in response to measured changes incontrolled process variables. The adaptive controller employs an optimalfiltering technique wherein a weighted average of a predicted value forthe true state of the controlled variable obtained from a process modeland a measured value of the controlled process variable are used as theinput to a process controller to effect adjustment of the manipulatedprocess variable. Thus, the controller is enabled to respond to changescaused by process upsets but in substantially insensitive to measurementnoise.

Compensation for changes in process behavior is ef-' fected by adjustingtheprocess model which provides the predicted value for the controlledprocess variable. Consequently, the controller is self-adaptive and theprocess can be reidentified while the process is under closed loopcontrol.

Thus, by this self-compensating feature, realized through the adjustmentof the process model, the adaptive controller of the present inventionis more readily adaptable for use in many different types of processeswithout the need for initially providing a detailed model which definesthe functional relationship between a controlled process variable and amanipulated process variable in the process control loop.

What is claimed is:

1. In a closed loop process control system for a process, the method ofcontrolling process apparatus to maintain a controlled process variable(Y) at a predetermined value, said method comprising the steps ofproviding information in a stored mathematical model representing afunctional relationship between said controlled variable (Y) and amanipulated process variable (X), deriving a predicted value (Y(k/k-lfor the controlled variable from said mathematical model, obtainingmeasurements of the value of the controlled variable at periodicsampling intervals, deriving an estimated value (Y(k/k)) for saidcontrolled variable from the predicted value and a measured value (k) ofsaid controlled variable, calculating an adjusted value (X(k)) for saidmanipulated variable using the estimated value of said controlledvariable, and adjusting the value of said manipulated variable tocorrespond to said adjusted value and thereby effect a correspondingchange in the value of said controlled variable.

2. The method as set forth in claim 1 including the further step ofadjusting the mathematical model at the time of deriving the estimatedvalue (Y(k/k)) using the predicted value (Y(k/k-l last derived from themathematical model and the estimated value (Y(k/k)) last derived tocompensate for changes in operating conditions of the process.

3. The method as set forth in claim 2 wherein adjusting the mathematicalmodel includes the steps of comparing the last predicted value (Y(k/k1))to a previous estimated value (Y(kl/k-1 which was derived from apreceding measurement (Z(k-l and adjusting the mathematical modelwhenever the last predicted value differs from the previous estimatedvalue by more than a predetermined amount.

4. The method as set forth in claim 3, wherein the last predicted value(Y(k/k-l of the controlled variable is adjusted towards the last derivedestimated value (Y(k/k)) of the controlled variable whenever themathematical model is adjusted.

5. The method as set forth in claim 1, wherein the estimated value(Y(k/k)) for the controlled variable (Y) is defined by the relationship:

Y (k/k) Y (k/k-l) W [Z (k) Y (k/kl)] where Y (k/k-l) is the predictedvalue for the controlled variable Z(k) is the measured value for thecontrolled variable, and W is a noise weighting factor.

6. The method asset forth in claim 1, wherein calculating the adjustedvalue (X(k)) for said manipulated variable (X) includes the step ofcomparing the estimated value (Y(k/k)) to a desired set point value(R(k)) for the controlled variable (Y) to obtain a set point error value(E(k)) representing the difference between said estimated value and saidset point value.

7. The method as set forth in claim 6, wherein calculating the adjustedvalue (X(k)) for said manipulated variable (X) includes the step ofproviding information in a stored process controller representing thefunctional relationship (kl) (1-0) X (k-F-l) wherein E(k) is the valuefor the set point error calculated at the time of deriving the estimatedvalue Y(k/k).

E(k-l) is the value of the set point error calculated at the time ofderiving a previous estimated value Y(kl/k--l) which was derived from apreceding measurement.

X(k-l is the adjusted value calculated from the previous estimated valueY(kl/k-l X(k-I1) is the value of X(k) calculated F+ 1) measurements ago.

K is the gain of the process controller, and 17 and 6 are exponentialfunctions of the open and closed loop time constants respectively, ofthe process control system.

i. The rnethod as set forth in claim 1, wherein said mathematical modelstores information representing the functional relationship:

lWii'i'iKWk/k-1 is the predicted value for the controlled variable lastderived from the mathematical model.

YUt-d/k-l) is a previous estimated value for the controlled variablederived at'the time the last predicted value was derived.

Y(k2/k 2) is a further previous estimated value for the controlledvariable derived prior to the time of deriving the last predicted value.

AX (k-F-l) is the difference between successive valuesof the manipulatedvariable calculated prior to the time'of deriving the last predictedvalue.

1" is a dead time factor.

K is the gain of the mathematical process model, and

r is an exponential function of the open loop time constant of theprocess control system.

9. In a process control system for a process, measuring means formeasuring a controlled process variable and providing signalsrepresenting a measured value of the controlled variable, means forstoring data representing a predicted value for said controlledvariable, process apparatus for controlling the value of said controlledvariable as a function of the set point of said process apparatus, andprocess controller means responsive to said signals for controlling saidprocess apparatus to compensate for changes in the value of saidcontrolled variable caused by process upsets,said process controllermeans comprising signal processing means programmed to provide furthersignals from said stored data representing a predicted value and tocalculate an adjusted set point value for said process apparatus from aweighted average of the predicted and measured values of said controlledvariable represented by said signals.

10. In a closed loop process control system for a pro cess, measuringmeans for measuring the value of a controlled process variable (Y) andproviding first output signals representing the value (Z(k)) of saidcontrolled variable, system control means responsive to said firstoutput signals for maintaining said controlled variable (Y) at apredetermined value (R(k)) by adjusting the value of a manipulatedprocess variable (X) to effect a corresponding adjustment in the valueof said controlled variable deviates from said predetermined value, saidsystem control means comprising mathematical model means storinginformation for establishing a reference value for said controlledprocess variable and providing second output signals representing apredicted value (Y(k/k-l for said controlled variable, filter meansresponsive to said first and second output signals to provide thirdoutput signals representing an estimated value (Y(k/k)) for saidcontrolled process variable and controller means responsive to saidthird output signals to calculate an adjusted value (X(k)) for saidmanipulated variable.

11, In a"pasermaiiiiaamiiag"siseeg roces apparatus for manufacturing acontinuous paper sheet having a predetermined weight, measuring meansfor measuring the weight of said paper and providing first outputsignals representing the weight (Z(k)) of said paper sheet, systemcontrol means including mathematical process model means storinginformation for establishing a reference value for the weight of saidpaper sheet and for providing second output signals representing apredicted value (Y(k/k-l for the weight of said paper sheet, filtermeans responsive to said first and second output signals to providethird output signals representing an estimated value (Y(k/k)) for theweight of said paper sheet, and controller means responsive to saidthird output signals for providing control signals to said processapparatus for effecting adjustment of the weight value of said papersheet whenever the measured value of the weight of said paper sheetdeviates from said desired value.

12. System control means as set forth in claim 11, wherein saidmathematical process model means includes logic means for comparing thesecond output signals representing said predicted value (Y(k/kl)) withthe third output signals representing said estimated value (Y(k/k)) andeffecting adjustment of a predicted value toward said estimated value.

13. In a paper manufacturing process, apparatus for manufacturing acontinuous sheet of paper from liquid stock, measuring means formeasuring the weight of said paper sheet and providing first outputsignals representing the measured value of the weight of said papersheet, valve means for controlling the flow rate of said liquid stock tosaid apparatus as a function of the set point of said valve means toestablish a predeter mined weight for said paper sheet, and systemcontrol means including mathematical process model means for providingsecond output signals representing a predicted value for the dry basisweight of said paper sheet, filter means responsive to said first andsecond output signals for providing third output signals representing anestimated value for said dry basis weight, controller means responsiveto said third output signals to provide fourth output signalsrepresenting an adjusted set point value for the stock flow valve means,and output means responsive to said fourth output signals to providecontrol signals for said stock flow means for adjusting the set point ofsaid stock flow valve means whenever the measured value of the dry basisweight deviates from a desired value due to a process upset.

14. In a paper manufacturing process, apparatus for manufacturing acontinuous sheet of paper from liquid stock including head box means forcontaining liquid stock and for depositing said liquid stock on conveyormeans in a continuous paper web, measuring means for measuring the basisweight and moisture content of said paper web to provide first outputsignals representing a measured value of the dry basis weight of saidpaper web, stock flow valve means for controlling the flow rate ofliquid stock through said head box means as a function of the set pointof said stock flow valve means to thereby control the basis weight ofsaid paper web, and system control means comprising mathematical processmodel means for providing second output signals representing a predictedvalue for the dry basis weight of said paper web, filter meansresponsive to said first and second output signals for providing thirdoutput signals representing an estimated value for said dry basis weightof said paper web, and controller means responsive to said third outputsignals for computing an adjusted set point value for said stock flowvalve means to provide control signals for said stock flow valve meansfor adjusting the set point of said stock flow valve means whenever themeasured value of the dry basis weight deviates from a desired value dueto a process upset.

15. In a paper manufacturing process, apparatus for manufacturing acontinuous sheet of paper from liquid stock including head box means forcontaining liquid stock and for depositing said liquid stock on conveyormeans in a continuous web, dryer means for removing moisture from saidpaper web as said paper web is moved by said conveyor means from saidhead box means totake-up reel means, steam valve means for regulatingthe drying process of said dryer means, measuring means for measuringthe moisture content of said paper web to provide first output signalsrepresenting the measured value of the moisture content of said paperweb, and system control means comprising mathematical process modelmeans for providing second output signals representing a predicted valuefor the moisture content of said paper web, filter means responsive tosaid first and second output signals for providing third output signalsrepresenting an estimated value for the moisture content of said paperweb, and controller means responsive to said third output signals forcalculating an adjusted set point value for said steam valve means toprovide control signals to said steam valve means for adjusting the setpoint of said steam valve means whenever the measured value of themoisture content of said paper sheet deviates from a desired value dueto a process upset.

1. In a closed loop process control system for a process, the method ofcontrolling process apparatus to maintain a controlled process variable(Y) at a predetermined value, said method comprising the steps ofproviding information in a stored mathematical model representing afunctional relationship between said controlled variable (Y) and amanipulated process variable (X), deriving a predicted value (Y(k/k-1))for the controlled variable from said mathematical model, obtainingmeasurements of the value of the controlled variable at periodicsampling intervals, deriving an estimated value (Y(k/k)) for saidcontrolled variable from the predicted value and a measured value (k) ofsaid controlled variable, calculating an adjusted value (X(k)) for saidmanipulated variable using the estimated value of said controlledvariable, and adjusting the value of said manipulated variable tocorrespond to said adjusted value and thereby effect a correspondingchange in the value of said controlled variable.
 2. The method as setforth in claim 1 including the further step of adjusting themathematical model at the time of deriving the estimated value (Y(k/k))using the predicted value (Y(k/k-1)) last derived from the mathematicalmodel and the estimated value (Y(k/k)) last derived to compensate forchanges in operating conditions of the process.
 3. The method as setforth in claim 2 wherein adjusting the mathematical model includes thesteps of comparing the last predicted value (Y(k/k-1)) to a previousestimated value (Y(k-1/k-1)) which was derived from a precedingmeasurement (Z(k-1)) and adjusting the mathematical model whenever thelast predicted value differs from the previous estimated value by morethan a predetermined amount.
 4. The method as set forth in claim 3,wherein the last predicted value (Y(k/k-1)) of the controlled variableis adjusted towards the last derived estimated value (Y(k/k)) of thecontrolled variable whenever the mathematical model is adjusted.
 5. Themethod as set forth in claim 1, wherein the estimated value (Y(k/k)) forthe controlled variable (Y) is defined by the relationship: Y (k/k) Y(k/k-1) + W (Z (k) - Y (k/k-1)) where Y (k/k-1) is the predicted valuefor the controlled variable Z(k) is the measured value for thecontrolled variable, and W is a noise weighting factor.
 6. The method asset forth in claim 1, wherein calculating the adjusted value (X(k)) forsaid manipulated variable (X) includes the step of comparing theestimated value (Y(k/k)) to a desired set point value (R(k)) for thecontrolled variable (Y) to obtain a set point error value (E(k))representing the difference between said estimated value and said setpoint value.
 7. The method as set forth in claim 6, wherein calculatingthe adjusted value (X(k)) for said manipulated variable (X) includes thestep of providing information in a stored process controllerrepresenting the functional relationship X (k) ((1 - theta )/K(1- eta ))(E(k) - eta E (k-1)) + theta X (k-1) + (1- theta ) X (k- Gamma -1)wherein E(k) is the value for the set point error calculated at the timeof deriving the estimated value Y(k/k); E(k-1) is the value of the setpoint error calculated at the time of deriving a previous estimatedvalue Y(k-1/k-1) which was derived from a preceding measurement; X(k-1)is the adjusted value calculated from the previous estimated valueY(k-1/k-1); X(k- Gamma -1) is the value of X(k) calculated ( Gamma + 1)measurements ago; K is the gain of the process controller, and eta andtheta are exponential functions of the open and closed loop timeconstants respectively, of the process control system.
 8. The method asset forth in claim 1, wherein said mathematical model stores informationrepresenting the functional relationship: Y(k/k-1) + Y(k-1/k-1) + K(1-eta ) Delta X(k- Gamma -1) + eta Y(k-1/k-1) + Y(k-2/k-2) eta whereinY(k/k-1) is the predicted value for the controlled variable last derivedfrom the mathematical model; Y(k-1/k-1) is a previous estimated valuefor the controlled variable derived at the time the last predicted valuewas derived; Y(k-2/k-2) is a further previous estimated value for thecontrolled variable derived prior to the time of deriving the lastpredicted value; Delta X (k- Gamma -1) is the difference betweensuccessive values of the manipulated variable calculated prior to thetime of deriving the last predicted value; Gamma is a dead time factor;K is the gain of the mathematical process model, and eta is anexponential function of the open loop time constant of the processcontrol system.
 9. In a process control system for a process, measuringmeans for measuring a controlled process variable and providing signalsrepresenting a measured value of the controlled variable, means forstoring data representing a predicted value for said controlledvariable, process apparatus for controlling the value of said controlledvariable as a function of the set point of said process apparatus, andprocess controller means responsive to said signals for controlling saidprocess apparatus to compensate for changes in the value of saidcontrolled variable caused by process upsets,said process controllermeans comprising signal processing means programmed to provide furthersignals from said stored data representing a predicted value and tocalculate an adjusted set point value for said process apparatus from aweighted average of the predicted and measured values of said controlledvariable represented by said signals.
 10. In a closed loop processcontrol system for a process, measuring means for measuring the value ofa controlled process variable (Y) and providing first output signalsrepresenting the value (Z(k)) of said controlled variable, systemcontrol means responsive to said first output signals for maintainingsaid controlled variable (Y) at a predetermined value (R(k)) byadjusting the value of a manipulated process variable (X) to effect acorresponding adjustment in the value of said controlled variabledeviates from said predetermined value, said system control meanscomprising mathematical model means storing information for establishinga reference value for said controlled process variable and providingsecond output signals representing a predicted value (Y(k/k-1)) for saidcontrolled variable, filter means responsive to said first and secondoutput signals to provide third output signals representing an estimatedvalue (Y(k/k)) for said controlled process variable and controller meansresponsive to said third output signals to calculate an adjusted value(X(k)) for said manipulated variable.
 11. In a paper manufacturingprocess, process apparatus for manufacturing a continuous paper sheethaving a predetermined weight, measuring means for measuring the weightof said paper and providing first output signals representing the weight(Z(k)) of said paper sheet, system control means including mathematicalprocess model means storing information for establishing a referencevalue for the weight of said paper sheet and for providing second outputsignals representing a predicted value (Y(k/k-1)) for the weight of saidpaper sheet, filter means responsive to said first and second outputsignals to provide third output signals representing an estimated value(Y(k/k)) for the weight of said paper sheet, and controller meansresponsive to said third output signals for providing control signals tosaid process apparatus for effecting adjustment of the weight value ofsaid paper sheet whenever the measured value of the weight of said papersheet deviates from said desired value.
 12. System control means as setforth in claim 11, wherein said mathematical process model meansincludes logic means for comparing the second output signalsrepresenting said predicted value (Y(k/k-1)) with the third outputsignals representing said estimated value (Y(k/k)) and effectingadjustment of a predicted value toward said estimated value.
 13. In apaper manufacturing process, apparatus for manufacturing a continuoussheet of paper from liquid stock, measuring means for measuring theweight of said paper sheet and providing first output signalsrepresenting the measured value of the weight of said paper sheet, valvemeans for controlling the flow rate of said liquid stock to saidapparatus as a function of the set point of said valve means toestablish a predetermined weight for said paper sheet, and systemcontrol means including mathematical process model means for providingsecond output signals representing a predicted value for the dry basisweight of said paper sheet, filter means responsive to said first andsecond output signals for providing third output signals representing anestimated value for said dry basis weight, controller means responsiveto said third output signals to provide fourth output signalsrepresenting an adjusted set point value for the stock flow valve means,and output means responsive to said fourth output signals to providecontrol signals for said stock flow means for adjusting the set point ofsaid stock flow valve means whenever the measured value of the dry basisweight deviates from a desired value due to a process upset.
 14. In apaper manufacturing process, apparatus for manufacturing a continuoussheet of paper from liquid stock including head box means for containingliquid stock and for depositing said liquid stock on conveyor means in acontinuous paper web, measuring means for measuring the basis weight andmoisture content of said paper web to provide first output signalsrepresenting a measured value of the dry basis weight of said paper web,stock flow valve means for controlling the flow rate of liquid stockthrough said head box means as a function of the set point of said stockflow valve means to thereby control the basis weight of said paper web,and system control means comprising mathematical process model means forproviding second output signals representing a predicted value for thedry basis weight of said paper web, filter means responsive to saidfirst and second output signals for providing third output signalsrepresenting an estimated value for said dry basis weight of said paperweb, and controller means responsive to said third output signals forcomputing an adjusted set point value for said stock flow valve means toprovide control signals for said stock flow valve means for adjustingthe set point of said stock flow valve means whenever the measured valueof the dry basis weight deviates from a desired value due to a processupset.
 15. In a paper manufacturing process, apparatus for manufacturinga continuous sheet of paper from liquid stock including head box meansfor containing liquid stock and for depositing said liquid stock onconveyor means in a continuous web, dryer means for removing moisturefrom said paper web as said paper web is moved by said conveyor meansfrom said head box means tO take-up reel means, steam valve means forregulating the drying process of said dryer means, measuring means formeasuring the moisture content of said paper web to provide first outputsignals representing the measured value of the moisture content of saidpaper web, and system control means comprising mathematical processmodel means for providing second output signals representing a predictedvalue for the moisture content of said paper web, filter meansresponsive to said first and second output signals for providing thirdoutput signals representing an estimated value for the moisture contentof said paper web, and controller means responsive to said third outputsignals for calculating an adjusted set point value for said steam valvemeans to provide control signals to said steam valve means for adjustingthe set point of said steam valve means whenever the measured value ofthe moisture content of said paper sheet deviates from a desired valuedue to a process upset.
 16. In a paper manufacturing process, apparatusfor manufacturing a continuous sheet of paper from liquid stock, valvemeans for providing liquid stock to said apparatus at a predeterminedflow rate, drying means for removing moisture from said paper sheet at apredetermined drying rate, measuring means for providing measurements ofthe basis weight and the moisture content of said paper sheet, andsystem control means including basis weight controller means forderiving from said measurements a first estimated value for the drybasis weight of said paper and comparing said first estimated value to adry stock flow set point to provide control signals for said valve meansfor adjusting the flow rate of said liquid stock whenever the dry basisweight of said paper sheet deviates from a desired weight, and moisturecontroller means for deriving from said measurements a second estimatedvalue for the moisture content of said paper sheet and comparing saidsecond estimated value to a moisture content set point to providefurther control signals for said drying means for adjusting the dryingrate of said drying means whenever the moisture content of said papersheet deviates from a desired amount.
 17. In a paper manufacturingprocess for manufacturing a continuous paper sheet from liquid stock, aclosed loop process control system comprising dry stock flow controllermeans connected in a first control loop for comparing a value of drystock flow to a dry stock flow set point and calculating an adjustedvalue for a set point for a stock flow valve whenever the dry stock flowdiffers from the dry stock flow set point, and basis weight controllermeans connected in a second control loop which includes said firstcontrol loop for comparing a value for the dry basis weight of saidpaper sheet obtained from measurements to a dry basis weight set pointand calculating an adjusted value for the dry stock flow set point forsaid dry stock flow controller means whenever the dry basis weightdiffers from the dry basis weight set point.
 18. In a papermanufacturing process for manufacturing a continous paper sheet themethod of controlling process apparatus to maintain the weight of saidpaper sheet at a predetermined value, said method comprising the stepsof deriving a value of the dry basis weight of said paper sheet frommeasured values of the basis weight and the moisture content of saidpaper sheet, calculating a dry stock flow set point using the derivedvalue for said dry basis weight, calculating the dry stock flow rate,comparing the dry stock flow set point to the dry stock flow rate,calculating an adjusted value for the set point of valve means of saidprocess apparatus whenever the difference between the dry stock flow setpoint and the dry stock flow rate exceeds a predetermined amount, andproviding control signals to said process apparatus for changing the setpoint of said valve means to said adjusted value.
 19. The method as setforth in claim 18, wherein calculating the dry stock flow set pointincludes providing the functional relationship between the dry basisweight and the dry stock flow set point in a stored mathematical model,deriving a predicted value for the dry basis weight from saidmathematical model, calculating an estimated value for the dry basisweight from said predicted value and the dry basis weight value obtainedby said measurements, and using said estimated value to calculate saiddry stock flow set point.
 20. In a paper manufacturing process formanufacturing a continuous sheet of paper, the method of controllingprocess apparatus to maintain the weight of said paper sheet at apredetermined value, said method comprising the steps of establishing ina stored mathematical model the functional relationship between theweight of said paper sheet and a set point (R(k)) for a control valve ofsaid process apparatus, deriving a predicted value (Y(k/k-1)) for theweight of said paper sheet from said mathematical model, deriving anestimated value (Y(k/k)) for the weight of said paper sheet from thepredicted value and a measured value (Z(k)) for the weight of said papersheet obtained from a measurement, calculating an adjusted value (X(k))for the set point for said valve means using said estimated value toobtain the set point required for said valve means to provide a desiredweight for said paper sheet, and providing control signals for saidprocess apparatus for changing the set point of said valve means to saidadjusted value.
 21. The method as set forth in claim 20, which includesa further step of adjusting the mathematical model at the time ofderiving the estimated value, including comparing the predicted value(Y(k/k-1)) last derived from the mathematical model to a previousestimated value (Y(k-1/k-1)) which was derived from a precedingmeasurement, and adjusting the mathematical model whenever the lastpredicted value (Y(k/k-1)) is less than or greater than the previousestimated value (Y(k-1/k-1)) by a predetermined amount.
 22. The methodas set forth in claim 21, wherein the resultant adapting of themathematical model includes adjusting the last predicted value(Y(k/k-1)) towards the last derived estimated value (Y(k/k)).
 23. Themethod as set forth in claim 22, wherein the mathematical model ischaracterized by a predetermined gain (G) and wherein the gain of saidmathematical model is adjusted as a function of the value of the lastpredicted value (Y(k/k-1)) relative to the value of the last estimatedvalue (Y(k/k)).
 24. The method as set forth in claim 23, wherein thegain of the mathematical model is increased whenever the last predictedvalue (Y(k/k-1)) is less than the last estimated value (Y(k/k)) and thegain of the mathematical model is decreased whenever the last predictedvalue (Y(k/k-1)) is greater than the last estimated value (Y(k/k)) suchthat with each gain change a future predicted value (Y(k + 1/k)) derivedfrom the stored mathematical model will approach the estimated value.25. The method as set forth in claim 23, wherein the adjustment of saidmathematical model includes calculating a gain factor and adjusting thegain in predetermined increments of said gain factor.
 26. The method asset forth in claim 25, wherein the gain of said mathematical model isadjusted in increments of two per cent of the gain factor.
 27. Themethod as set forth in claim 25, wherein the gain is adjusted withinpredetermined limits.
 28. The method as set forth in claim 21, whereinthe derivation of the last estimated value (Y(k/k)) for the weight ofthe paper sheet includes calculating a weighted average of the lastpredicted value (Y(k/k-1)) and the measured value (Z(k)) of the weightof said paper sheet.